Consider 7 items along their respective weights and values I = I1, I2, I3, I4, I5, I6, I7 W = 2,3,5,7,1,4,1 V = 10,5,15,7,6,18,3 The capacity of knapsack W=15. Find the optimal solution of the fractional knapsack problem. What is the complexity of finding the solution of fractional knapsack problem?

Please solve..

Consider the following version of Knapsack. Given are two weight limits W 1 and W 2 , whereW 1 ≤ W 2 . Given are also n items (w 1 , c 1 ), (w 2 , c 2 ), . . . , (w n , c n ), where w i is the weight and c ithe cost of the i-th item. We want to find a subset of these items of the highest cost, wherethe subset weights at least W 1 and at most W 2 . Give an O(nW 2 ) algorithm for this problem.(Recall that the cost (respectively weight) of a subset is the sum of the costs (respectivelyweights) of the items in the subset.)

Find an optimal Hoffman code for g:5, o:15, u:28, m:25, b:10, c:17. draw out steps so i can understand

n For n distinct elements a₁,..., an with positive weights w₁,..., wn s.t. -1 W₁ = 1, design a linear-time algorithm returning the element ak, which satisfies the following: Σ w₁ ≤ 1/2 and Σ wi ≤ 1/2. ai ak Assume that such an ak always exists. You should also justify the time complexity.

Using LDA, compute the optimal projection line in a single dimension, for two labelled sets of 2- dimensional points given below: Class 1 = { (1,0), (1,2), (3,0), (3,2)} Class 2 = { (2,4), (3,2), (5,4), (6,2)}

Solve By  greedy algorithm

Cse

Correct answer will be upvoted else downvoted. Computer science.    Polycarp can cut any piece of paper w×h that he has in just two cases:    On the off chance that w is even, he can slice the sheet down the middle and get two sheets of size w2×h;    In the event that h is even, he can slice the sheet down the middle and get two sheets of size w×h2;    On the off chance that w and h are even simultaneously, Polycarp can slice the sheet as indicated by any of the standards above.    In the wake of cutting a piece of paper, the complete number of pieces of paper is expanded by 1.    Assist Polycarp with seeing whether he can cut his sheet of size w×h at into n or more pieces, utilizing just the principles portrayed previously.    Input    The principal line contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow.    Each experiment comprises of one line containing three integers w, h, n (1≤w,h≤104,1≤n≤109) — the width and stature of the…